Publication details

Submaximally symmetric quaternion Hermitian structures

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Authors

KRUGLIKOV Boris WINTHER Henrik

Year of publication 2020
Type Article in Periodical
Magazine / Source International Journal of Mathematics
MU Faculty or unit

Faculty of Science

Citation
Web https://doi.org/10.1142/S0129167X20500846
Doi http://dx.doi.org/10.1142/S0129167X20500846
Keywords Symmetry dimension; automorphism group; quaternion-Hermitian manifolds; the gap phenomenon; Wolf space; quaternion-Kahler structure
Description We consider and resolve the gap problem for almost quaternion-Hermitian structures, i.e. we determine the maximal and submaximal symmetry dimensions, both for Lie algebras and Lie groups, in the class of almost quaternion-Hermitian manifolds. We classify all structures with such symmetry dimensions. Geometric properties of the submaximally symmetric spaces are studied, in particular, we identify locally conformally quaternion-Kahler structures as well as quaternion-Kahler with torsion.
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